Error Compensation For Complex Surfaces Machining Based On Cutting Forces Modeling

Complex surfaces have been widely used in aerospace, automotive and die/mold industries, because of their excellent functional properties and appearence. These kinds of surfaces are required to have high requirements on dimensional precision and surface quality. Multi-axis CNC machine tools are usually used for complex surfaces machining, and ball-end mills are usually used in semi-finish and finish milling processes. The surface quality includes surface precision, surface roughness, surface residual stress and surface work hardening etc. Complex surfaces and especially the surfaces with non-single curvature are seldom investigated. Among them, little overall and systematic research, especially the research on surface error due to cutting force-induced tool deflections has been made, and these surface errors are closely related with the geometric features of complex surfaces. In this dissertation, by analysising the geometric features of complex surfaces and the kinematics of multi-axis ball-end milling process synthetically, the relationships among surface precision, curvature radius, cutter orientation and cutting parameters have been thoroughly analyzed. The error compensation method and tool path direction selection method for high surface precision have been proposed. It is an important foundation subject for precision control in multi-axis ball-end milling.The solving methods for curvature radius of complex surfaces are discussed separately. Considering the curvature radius and tool inclination angle, the theoretical-model and simulation of cutting forces on multi-axis ball-end milling of complex surfaces are carried. According to the characteristic of multi-axis ball-end milling, equations to estimate the cutting forces at a differential element on the cutting edge are established based on the instantaneous cutting force model proposed by Lee and Altintas. Start/exit radial immersion angles and limit axial position angles are solved using analytical geometry method taking into account the curvature radius and tool inclination angle, and then contact areas between cutter and workpiece are obtained. The mappings among all related coordinate of DMU-70V vertical machining center are modeled,3-dimensional cutting forces were modeled and simulated using Matlab software. The simulation results show the influence of curvature radius and tool inclination angle on the cutting forces in the X, Y, Z directions. It provides the reliable theoretical basis for the subsequent prediction and control of surface precision.The cutting forces are simplified to concentrated forces which act on a point of cutter-workpiece contact area. The deflections of action points of concentrated forces in the X, Y directions are cutting force-induced tool deflections. Different from the traditional two segments cantilever beam tool deflection model, addressing the three parts (shank, flute-non ball-end and ball-end parts) of ball-end mill, three segments cantilever beam tool deflection model was built using materials mechanics method for ball-end mill. The comparison results show that, the tool deflection magnitude calculated by the new three segments method match better with the results of ANSYS 12.0 Workbench method than the results of the traditional two segments. Cutter eccentricity has an important impact on cutting forces through acting on feed per tooth, effective cutting radius and tool rotation angle. Then the extended researches on the cutting force model of complex surfaces were explored based on the three segments cantilever beam tool deflection model and the extended research on cutter eccentricity.Based on tool deflection values of the acting point of force in the X, Y directions, for arbitrary point of tool path in the workpiece local coordinate system, the complex surfaces error model in the normal direction was established. After the error modeling, the error compensation was finished using iterative algorithm on every CL point based on the features analysis of multi-axis ball-end milling of complex surfaces. A typical sinusoidal surface was chosen for tool deflection error modeling, and off-line error compensation of the tool path file was finished. The results show that the tool paths after error compensation match better with the designed ones than those without error compensation. Different from the case of 3-axis milling, the tool deflection in multi-axis milling could decrease by choosing not only the best tool path direction based on the analysis of curvature radius of different tool path direction, but also the best tool inclination angle. In this dissertation, the relationship between step length and path internal with the curvature radius was discussed separately for three surface types (plane, convex and concave surface). For getting high precision, the selection of tool path direction was discussed for three typical tool path generation methods (iso-parametric, iso-planar and iso-scallop method). Through analyzing the relationship between tool deflections in the X, Y directions and surface normal error with the tool inclination angle, selecting the tool inclination angle as small as possible is best for high suface precision. An example was presented to verify the newly proposed iso-scallop method for tool path generation, the results show that the cutting time could decrease with the new method. For different initial tool paths, the different average curvature radii in the direction perpendicular to the tool path could result in different surface normal errors.